Identifier
Values
([],1) => ([(0,1)],2) => [1] => 0
([],2) => ([(0,2),(1,2)],3) => [2] => 0
([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => [3] => 0
([],3) => ([(0,3),(1,3),(2,3)],4) => [3] => 0
([(1,2)],3) => ([(0,3),(1,2),(1,3),(2,3)],4) => [4] => 0
([(0,2),(1,2)],3) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [5] => 0
([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [6] => 0
([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => [4] => 0
([(2,3)],4) => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => [5] => 0
([(1,3),(2,3)],4) => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [6] => 0
([(0,3),(1,3),(2,3)],4) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [7] => 0
([(0,3),(1,2)],4) => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => [6] => 0
([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => [7] => 0
([(1,2),(1,3),(2,3)],4) => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [7] => 0
([(0,3),(1,2),(1,3),(2,3)],4) => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [8] => 0
([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => [8] => 0
([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [5] => 0
([(3,4)],5) => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 0
([(2,4),(3,4)],5) => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [7] => 0
([(1,4),(2,4),(3,4)],5) => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [8] => 0
([(1,4),(2,3)],5) => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [7] => 0
([(1,4),(2,3),(3,4)],5) => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => [8] => 0
([(0,1),(2,4),(3,4)],5) => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [8] => 0
([(2,3),(2,4),(3,4)],5) => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [8] => 0
([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6] => 0
([(4,5)],6) => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 0
([(3,5),(4,5)],6) => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [8] => 0
([(2,5),(3,4)],6) => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [8] => 0
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searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
Description
Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight.
Given $\lambda$ count how many integer compositions $w$ (weight) there are, such that
$P_{\lambda,w}$ is non-integral, i.e., $w$ such that the Gelfand-Tsetlin polytope $P_{\lambda,w}$ has at least one non-integral vertex.
See also St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight..
Each value in this statistic is greater than or equal to corresponding value in St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight..
Map
cone
Description
The cone of a graph.
The cone of a graph is obtained by joining a new vertex to all the vertices of the graph. The added vertex is called a universal vertex or a dominating vertex.
Map
to edge-partition of connected components
Description
Sends a graph to the partition recording the number of edges in its connected components.